Quantum Spring

When it comes to successful theories to explain the behavior of matter, quantum mechanics stands alone. It was developed in the 1920s by Erwin Schrödinger, Werner Heisenberg, Wolfgang Pauli, Paul Dirac, and many others. The practical implication of this theory is that it allows us to understand atoms, molecules, nuclei, and solids. Technologies directly resulting from the development of quantum mechanics include scanning tunneling microscopes, nanoscale machines, and quantum computers.

In 1926, Schrödinger developed the wave equation. When mathematically explaining a quantum system, one must take the solution related to the behavior of this system and apply certain boundary conditions to it. This tells us the allowed 'wavefunctions' and energy levels in the system. Reworking a wavefunction provides one with all the measurable characteristics of that system.

{Maxwell also used a wave equation to describe electromagnetic radiation (electromagnetic waves). Schrodinger showed us how atoms and molecules can also be expressed in terms of waves (wave function).}

The Schrödinger equation provides the most complete description that can be given to a physical system. It's wavefunction (or state vector) describes possible points in space which are mapped by complex numbers called probability amplitudes. In a nutshell, these amplitudes are the values of wavefunctions. By squaring the absolute value of these complex numbers (|ψ(x)|^2 ), we can determine the probability density (or probability distribution) of momentary states of matter, telling us where things are and how they are interacting. Heisenberg’s matrix mechanics are derived from Schrödinger's wavefunctions.

The actual equation (or a 1-dimensional, time-independent variation of it), given mass m confined to moving along the x-axis and interacting with its environment through a potential energy function u(x), is written:

Eψ=-(hbar^2/2m)[(d^2ψ)/dx^2:] + Uψ (hbar^2 = Plank's constant)

Time-dependent Schrödinger equations describe systems evolving with time, whereas time-independent describe stationary states. These equations can take on several different forms, depending on the physical situation. The equation doesn't break the principle of conservation of mechanical energy of a system. In fact, the first term in the above-mentioned Schrödinger equation reduces to the kinetic energy of the particle multiplied by the wave function, indicating that the total energy of a system is K + U = E = constant. Where total energy (E) is the sum of the kinetic energy (K) and the potential energy (U) - and the total energy is constant.

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Erwin Schrödinger had unconventional relationships with women. His American colleagues at Princeton were offended by the Austrian's 2 wives.

Schrödinger was an only child, and his mom was a chemistry professor. He died of tuberculosis in 1961. Upon realizing how fundamentally unintuitive quantum mechanics is, he is said to have proclaimed 'Verdammte Quantumspringerei!' (This damn quantum jumping!)

Derivation of TISE